2,801 research outputs found

    Statistics meets Machine Learning

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    Theory and application go hand in hand in most areas of statistics. In a world flooded with huge amounts of data waiting to be analyzed, classified and transformed into useful outputs, the designing of fast, robust and stable algorithms has never been as important as it is today. On the other hand, irrespective of whether the focus is put on estimation, prediction, classification or other purposes, it is equally crucial to provide clear guarantees that such algorithms have strong theoretical guarantees. Many statisticians, independently of their original research interests, have become increasingly aware of the importance of the numerical needs faced in numerous applications including gene expression profiling, health care, pattern and speech recognition, data security, marketing personalization, natural language processing, to name just a few. The goal of this workshop is twofold: (a) exchange knowledge on successful algorithmic approaches and discuss some of the existing challenges, and (b) to bring together researchers in statistics and machine learning with the aim of sharing expertise and exploiting possible differences in points of views to obtain a better understanding of some of the common important problems

    A discrete graph Laplacian for signal processing

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    In this thesis we exploit diffusion processes on graphs to effect two fundamental problems of image processing: denoising and segmentation. We treat these two low-level vision problems on the pixel-wise level under a unified framework: a graph embedding. Using this framework opens us up to the possibilities of exploiting recently introduced algorithms from the semi-supervised machine learning literature. We contribute two novel edge-preserving smoothing algorithms to the literature. Furthermore we apply these edge-preserving smoothing algorithms to some computational photography tasks. Many recent computational photography tasks require the decomposition of an image into a smooth base layer containing large scale intensity variations and a residual layer capturing fine details. Edge-preserving smoothing is the main computational mechanism in producing these multi-scale image representations. We, in effect, introduce a new approach to edge-preserving multi-scale image decompositions. Where as prior approaches such as the Bilateral filter and weighted-least squares methods require multiple parameters to tune the response of the filters our method only requires one. This parameter can be interpreted as a scale parameter. We demonstrate the utility of our approach by applying the method to computational photography tasks that utilise multi-scale image decompositions. With minimal modification to these edge-preserving smoothing algorithms we show that we can extend them to produce interactive image segmentation. As a result the operations of segmentation and denoising are conducted under a unified framework. Moreover we discuss how our method is related to region based active contours. We benchmark our proposed interactive segmentation algorithms against those based upon energy-minimisation, specifically graph-cut methods. We demonstrate that we achieve competitive performance
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